Question

A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Answer 1

There is 75% probability that Hanif will lose the game.

Explanation:

Number of outcomes on tossing a coin = 2

Whenever an experiment is repeated "r" times, the total number of outcomes is calculated as:

`n^(r)`

Here n is the number of outcomes of one event. Since for tossing of a coin, the number of outcomes for each event is 2, so n = 2

The experiment is performed 3 times, so r = 3

Therefore, the total number of outcomes for tossing a coin 3 times is:

`2^3 = 8` outcomes

Hanif wins if either of these two condition is met:

1) He gets all heads. There is only 1 outcome in 8 outcomes in which we can get all heads

2) He gets all tails. There is only 1 outcome in 8 outcomes in which we can get all tails.

Therefore, there are 2 possible outcomes for which Hanif will be the winner. On all other outcomes he will loose. Since total number of outcomes is 8, the number of outcomes for which Hanif will loose = 8 - 2 = 6 outcomes

We have to find the probability that Hanif will loose the game. Since, probability is defined as the ratio of desired outcomes to total number of outcomes, the probability that Hanif will loose the game will be:

`(6)/(8) =(3)/(4) =0.75=75\%`

Therefore, there is 75% probability that Hanif will lose the game.